Latest revision as of 23:58, 22 December 2016

The Hankel functions of the second kind are defined by $$H_{\nu}^{(2)}(z)=J_{\nu}(z)-iY_{\nu}(z),$$ where $J_{\nu}$ is the Bessel function of the first kind and $Y_{\nu}$ is the Bessel function of the second kind. Note the similarity of these functions to the Hankel functions of the first kind.

References

Hankel functions

Hankel $H_{\nu}^{(1)}$

Hankel $H_{\nu}^{(2)}$

Spherical Hankel $h_{\nu}^{(1)}$

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 <gallery>
-File:Complex hankel H2 sub 1.png|[[Domain coloring]] of [[analytic continuation]] of $H_1^{(2)}(z)$.
+File:Complex hankel H2 sub 1.png|[[Domain coloring]] of $H_1^{(2)}(z)$.
 </gallery>
 </div>